Applied Mathematics Publications

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Applied Mathematics Publications

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    Numerical Analysis of Couple Stress Nanofluid in Temperature Dependent Viscosity and Thermal Conductivity
    (Springer Nature, 2021-02-24) Dhlamini, M.; Mondal, H.; Sibanda, P.; Motsa, S.
    This communication reports on an innovative study of two-dimensional couple stress fluid 3 with effect of viscosity and conductivity. We proposed a new model based on temperature dependent variable thermal conductivity on kinetic theory. Our model assumes that thermal conductivity is a decreasing function of temperature rather than an increasing function. The effect of the three key parameters, viscosity, thermal conductivity and couple stress parameter are analyzed. The coupled non-linear system is further validated numerically using the spectral quasilinearization method. The method is found to be accurate and convergent. Increasing the temperature dependent parameter for viscosity is shown to reduce the heat mass transfer rates at the surface. Increasing thermal conductivity and the couple stress parameter increased the heat mass transfer rates on the boundary surface.
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    On Degree-Based Topological Indices for Strong Double Graphs
    (Hindawi, 2021-02-02) Rafiullah, M.; Siddiqui, H.M.A.; Siddiqui, M.K.; Dhlamini, M.
    A topological index is a characteristic value which represents some structural properties of a chemical graph. We study strong double graphs and their generalization to compute Zagreb indices and Zagreb coindices. We provide their explicit computing formulas along with an algorithm to generate and verify the results. We also find the relation between these indices. A 3D graphical representation and graphs are also presented to understand the dynamics of the aforementioned topological indices.
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    Combined Optimal Stopping and Mixed Regular-Singular Control of Jump Diffusions
    (Scientific Research Publishing, 2021-04-01) Kusaya, C.; Mandiudza, M.; Mwareya, N.; Matete, C.; Shambira, L.; Ngaza, N.
    In this paper, we examine a model that maximises dividend payments for an insurance company with a debt liability. We assume that the company has a policy to reinvest a proportion of its surplus cash before paying dividends to shareholders. We model the dynamics of the cash reserves as a jump-diffusion process. Combined optimal stopping and mixed regular-singular control of the jump-diffusion process is presented and investigated. In the paper, we show that when the premium rate is less than the liability rate , then the company should not get into business and the optimal dividend policy is to immediately pay out the initial cash reserve as dividends to shareholders. For the case , we show that the optimal risk management depends on the current level of the cash reserves. We demonstrate that the company’s optimal dividend policy is to pay out as dividends surplus cash above a predetermined threshold. We also present numerical examples to illustrate the results obtained.
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    On Topological Analysis of Entropy Measures for Silicon Carbides Networks
    (Wiley, 2021-11-05) Wang, X.L.; Siddiqui, M.K.; Kirmani, S.A.K.; Manzoor, S.; Ahmad, S.; Dhlamini, M.
    The silicon material has provoked and stimulated significant research concern to a considerable extent taking into account its marvelous mechanical, optical, and electronic properties. Naturally, silicons are semiconductors and are utilized in the formation of various materials. For example, it is used in assembling the electronic based gadgets. In this article, we have studied the 2D structure of silicon carbide Si2C3 − I[m, n] and Si2C3 − II[m, n] and then continued to discuss some degree grounded topological descriptors in association with their corresponding entropy measures. We extend this computation to the quantitative and pictorial comparisons which could be beneficial in the structure amendment for effective implementation.
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    An Analysis of Eccentricity-Based Invariants for Biochemical Hypernetworks
    (Wiley, 2021-10-06) Rashid, M.A.; Ahmad, S.; Siddiqui, M.K.; Manzoor, S.; Dhlamini, M.
    Biological proceedings are well characterized by solid illustrations for communication networks. The framework of biological networks has to be considered together with the expansion of infectious diseases like coronavirus. Also, the graph entropies have established themselves as the information theoretic measure to evaluate the architectural information of biological networks. In this article, we examined conclusive biochemical networks like t‐level hypertrees along with the corona product of hypertrees with path. We computed eccentricity‐based indices for the depiction of aforementioned theoretical frameworks of biochemical networks. Furthermore, explicit depiction of the graph entropies with these indices is also measured.